相关论文: Martingale Couplings and Bounds on the Tails of Pr…

We establish Hoeffding-type concentration inequalities for the low and high tail bounds of sums of exchangeable random variables. Our results exhibit an anti-symmetry in such tail bounds due to the assumption of exchangeability, a…

Comparing concentration properties of uniform sampling with and without replacement has a long history which can be traced back to the pioneer work of Hoeffding (1963). The goal of this short note is to extend this comparison to the case of…

We provide bounds on the tail probabilities for simple procedures that generate random samples _without replacement_, when the probabilities of being selected need not be equal.

Let $M_n= \fsu X1n$ be a sum of independent random variables such that $ X_k\leq 1$, $\E X_k =0$ and $\E X_k^2=\s_k^2$ for all $k$. Hoeffding 1963, Theorem 3, proved that $$\P{M_n \geq nt}\leq H^n(t,p),\quad H(t,p)= \bgl(1+qt/p\bgr)^{p +qt}…

We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…

It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much…

Using terminologies of information geometry, we derive upper and lower bounds of the tail probability of the sample mean. Employing these bounds, we obtain upper and lower bounds of the minimum error probability of the 2nd kind of error…

We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable.…

In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…

We consider a branching random walk in the non-boundary case where the additive martingale $W_n$ converges a.s. and in mean to some non-degenerate limit $W_\infty$. We first establish the joint tail distribution of $W_\infty$ and the global…

We present new sampling methods in finite population that allow to control the joint inclusion probabilities of units and especially the spreading of sampled units in the population. They are based on the use of renewal chains and…

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the…

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…

For the problem of estimating lower tail and upper tail copulas, we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method uses a multiplier bootstrap of the…

In this paper, we give an alternative proof of the fact that, when compounding a nonnegative probability distribution, convex ordering between the distributions of the number of summands implies convex ordering between the resulting…

Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…

In a seminal paper Biggins and Kyprianou \cite{BKy04} proved the existence of a non degenerate limit for the {\it Derivative martingale} of the branching random walk. As shown in \cite{Aid11} and \cite{Mad11}, this is an object of central…

For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…